Related papers: A multifractal random walk
Random Walk is a basic algorithm to explore the structure of networks, which can be used in many tasks, such as local community detection and network embedding. Existing random walk methods are based on single networks that contain limited…
For a random walk defined for a doubly infinite sequence of times, we let the time parameter itself be an integer-valued process, and call the orginal process a random walk at random time. We find the scaling limit which generalizes the…
We introduce a new class of asymmetric random walks on the one-dimensional infinite lattice. In this walk the direction of the jumps (positive or negative) is determined by a discrete-time renewal process which is independent of the jumps.…
While records and order statistics of independent and identically distributed (i.i.d.) random variables X_1, ..., X_N are fully understood, much less is known for strongly correlated random variables, which is often the situation…
Discrete multiplicative turbulent cascades are described using a formalism involving infinitely divisible random measures. This permits to consider the continuous limit of a cascade developed on a continuum of scales, and to provide the…
We discuss large deviation properties of continuous-time random walks (CTRW) and present a general expression for the large deviation rate in CTRW in terms of the corresponding rates for the distributions of steps' lengths and waiting…
The uncoupled Continuous Time Random Walk (CTRW) in one space-dimension and under power law regime is splitted into three distinct random walks: (rw_1), a random walk along the line of natural time, happening in operational time; (rw_2), a…
We review statistical properties of models generated by the application of a (positive and negative order) fractional derivative operator to a standard random walk and show that the resulting stochastic walks display slowly-decaying…
In this paper we consider a stochastic process that may experience random reset events which bring suddenly the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonous…
The combined Continuous Time Random Walk (CTRW) in position and momentum space is introduced, in the form of two coupled integral equations that describe the evolution of the probability distribution for finding a particle at a certain…
Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a…
We introduce a class of generative network models that insert edges by connecting the starting and terminal vertices of a random walk on the network graph. Within the taxonomy of statistical network models, this class is distinguished by…
Distribution of loops in a one-dimensional random walk (RW), or, equivalently, neutral segments in a sequence of positive and negative charges is important for understanding the low energy states of randomly charged polymers. We investigate…
In this note we study dynamical random walks (DRW) with internal states. We consider a particle which performs a dynamical random walk on $\mathbb{Z}$ and whose local dynamics is given by expanding maps. We provide sufficient conditions for…
A switching random walk, commonly known under the misnomer `oscillating random walk', is a real-valued Markov chain whose distribution of increments is determined by the sign of the current position. We explicitly identify an invariant…
We address the theory of records for integrated random walks with finite variance. The long-time continuum limit of these walks is a non-Markov process known as the random acceleration process or the integral of Brownian motion. In this…
We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition…
In this paper, we introduce hierarchical random walks at first. In this model, we use two types of random walkers, {global and local} walkers. The global walker chooses a local walker at every step, then the chosen local walker moves a…
We consider random walks on discrete state spaces, such as general undirected graphs, where the random walkers are designed to approximate a target quantity over the network topology via sampling and neighborhood exploration in the form of…
The foundations of the fractional diffusion equation are investigated based on coupled and decoupled continuous time random walks (CTRW). For this aim we find an exact solution of the decoupled CTRW, in terms of an infinite sum of stable…